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Combinatorial Property of a Special Polynomial Sequence

Published online by Cambridge University Press:  20 November 2018

L. Carlitz
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Leeming [4] has defined a sequence of polynomials {Q4n(x)} and a sequence of integers {Q4n} by means of

1

and

2

Thus

3

Leeming showed that the Q4n are all odd and that

4

It is proved in [3] that

5

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 20 , Issue 2 , 01 June 1977 , pp. 183 - 188
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Carlitz, L., Generating functions for a special class of permutations, Proceedings of the American Mathematical Society 47 (1975), 251-256.Google Scholar
2. Carlitz, L., Permutations with prescribed pattern, Mathematische Nachrichten 58 (1973), 31-53.Google Scholar
3. Carlitz, L., Some arithmetic properties of a special sequence of integers, Canadian Mathematical Bulletin, to appear.Google Scholar
4. Leeming, D. J., Some properties of a certain set of interpolation polynomials, Canadian Mathematical Bulletin 18(1975), 529-537.Google Scholar
5. Netto, E., Lehrbuch der Combinatorik, Teubner, Leipzig and Berlin, 1927.Google Scholar
6. Nörlund, N. E., Vorlesungen über Differenzenrechnung, Springer, Berlin, 1924 Google Scholar